7,938 research outputs found
Nonlocal Transformations for Accelerated Observers
According to the locality postulate of special relativity, the measurements
of physical fields by accelerated observers at a given event in Minkowski
spacetime are related to each other by the representations of the Lorentz
group. Nonlocal extensions of these representations are necessary, however,
once acceleration-induced nonlocality is taken into account. The particular
case of Dirac spinors is treated in detail and the corresponding nonlocal
transformation group is studied.Comment: 8 pages, accepted for publication in Ann. Phys. (Berlin
General formulation of Luria-Delbr{\"u}ck distribution of the number of mutants
The Luria-Delbr{\"u}ck experiment is a cornerstone of evolutionary theory,
demonstrating the randomness of mutations before selection. The distribution of
the number of mutants in this experiment has been the subject of intense
investigation during the last 70 years. Despite this considerable effort, most
of the results have been obtained under the assumption of constant growth rate,
which is far from the experimental condition. We derive here the properties of
this distribution for arbitrary growth function, for both the deterministic and
stochastic growth of the mutants. The derivation we propose uses the number of
wild type bacteria as the independent variable instead of time. The derivation
is surprisingly simple and versatile, allowing many generalizations to be taken
easily into account
Necessity of Acceleration-Induced Nonlocality
The purpose of this paper is to explain clearly why nonlocality must be an
essential part of the theory of relativity. In the standard local version of
this theory, Lorentz invariance is extended to accelerated observers by
assuming that they are pointwise inertial. This locality postulate is exact
when dealing with phenomena involving classical point particles and rays of
radiation, but breaks down for electromagnetic fields, as field properties in
general cannot be measured instantaneously. The problem is corrected in
nonlocal relativity by supplementing the locality postulate with a certain
average over the past world line of the observer.Comment: 12 pages; v2: improved version accepted for publication in Ann. Phys.
(Berlin
An alternative to the breeder's and Lande's equations
The breeder's equation is a cornerstone of quantitative genetics and is
widely used in evolutionary modeling. The equation which reads R=h^{2}S relates
response to selection R (the mean phenotype of the progeny) to the selection
differential S (mean phenotype of selected parents) through a simple
proportionality relation. The validity of this relation however relies strongly
on the normal (Gaussian) distribution of parent's genotype which is an
unobservable quantity and cannot be ascertained. In contrast, we show here that
if the fitness (or selection) function is Gaussian, an alternative, exact
linear equation in the form of R'=j^{2}S' can be derived, regardless of the
parental genotype distribution. Here R' and S' stand for the mean phenotypic
lag behind the mean of the fitness function in the offspring and selected
populations. To demonstrate this relation, we derive the exact functional
relation between the mean phenotype in the selected and the offspring
population and deduce all cases that lead to a linear relation between these
quantities. These computations, which are confirmed by individual based
numerical simulations, generalize naturally to the multivariate Lande's
equation \Delta\mathbf{\bar{z}}=GP^{-1}\mathbf{S}
Vacuum Electrodynamics of Accelerated Systems: Nonlocal Maxwell's Equations
The nonlocal electrodynamics of accelerated systems is discussed in
connection with the development of Lorentz-invariant nonlocal field equations.
Nonlocal Maxwell's equations are presented explicitly for certain linearly
accelerated systems. In general, the field equations remain nonlocal even after
accelerated motion has ceased.Comment: LaTeX file, 23 pages, no figures, accepted for publication in Annalen
der Physi
Neutral Aggregation in Finite Length Genotype space
The advent of modern genome sequencing techniques allows for a more stringent
test of the neutrality hypothesis of Darwinian evolution, where all individuals
have the same fitness. Using the individual based model of Wright and Fisher,
we compute the amplitude of neutral aggregation in the genome space, i.e., the
probability of finding two individuals at genetic (hamming) distance k as a
function of genome size L, population size N and mutation probability per base
\nu. In well mixed populations, we show that for N\nu\textless{}1/L, neutral
aggregation is the dominant force and most individuals are found at short
genetic distances from each other. For N\nu\textgreater{}1 on the contrary,
individuals are randomly dispersed in genome space. The results are extended to
geographically dispersed population, where the controlling parameter is shown
to be a combination of mutation and migration probability. The theory we
develop can be used to test the neutrality hypothesis in various ecological and
evolutionary systems
Gravitation and Nonlocality
The physical basis of the standard theory of general relativity is examined
and a nonlocal theory of accelerated observers is described that involves a
natural generalization of the hypothesis of locality. The nonlocal theory is
confronted with experiment via an indirect approach. The implications of the
results for gravitation are briefly discussed.Comment: LaTeX file, no figures, 12 pages. To be published in: Proc. 25th
Johns Hopkins Workshop "2001: A Relativistic Spacetime Odyssey" (World
Scientific, Singapore
Gravitoelectromagnetism
Gravitoelectromagnetism is briefly reviewed and some recent developments in
this topic are discussed. The stress-energy content of the
gravitoelectromagnetic field is described from different standpoints. In
particular, the gravitational Poynting flux is analyzed and it is shown that
there exists a steady flow of gravitational energy circulating around a
rotating mass.Comment: LaTeX file, no figures, 12 pages, Plenary talk given at EREs2000
(Valladolid, Spain, 6-9 September 2000); to be published in Proc. Spanish
Relativity Meeting, edited by J.-F. Pascual-S\'anchez, L. Flor\'ia, A. San
Miguel, and F. Vicente (World Scientific, 2001
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